# System Description: LEO - A Higher-Order Theorem Prover

@inproceedings{Benzmller1998SystemDL, title={System Description: LEO - A Higher-Order Theorem Prover}, author={Christoph Benzm{\"u}ller and Michael Kohlhase}, booktitle={CADE}, year={1998} }

Many (mathematical) problems, such as Cantor’s theorem, can be expressed very elegantly in higher-order logic, but lead to an exhaustive and un-intuitive formulation when coded in first-order logic. Thus, despite the difficulty of higher-order automated theorem proving, which has to deal with problems like the undecidability of higher-order unification (HOU) and the need for primitive substitution, there are proof problems which lie beyond the capabilities of first-order theorem provers, but…

## 94 Citations

Equality and extensionality in automated higher order theorem proving

- Computer Science
- 1999

The three new calculi ER, ERUE, EP and ERUE which improve the mechanisation of defined and primitvie equality in classical type theory and these calculi reach Henkin completeness without requiring additional extensionality axioms are introduced.

Extensional Higher-Order Paramodulation in Leo-III

- Computer ScienceJ. Autom. Reason.
- 2021

Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice that supports reasoning in polymorphic first-order and higher-order logic, in all normal quantified modal logics, as well as in different deontic logics.

An Adaptation of Paramodulation and Rue-resolution to Higher-order Logic

- Computer Science
- 1998

This techreport presents two approaches to primitive equality treatment in higher-order (HO) automated theorem proving: a calculus EP adapting traditional rst-order (FO) paramodulation RW69] , and a…

Can a Higher-Order and a First-Order Theorem Prover Cooperate?

- Computer ScienceLPAR
- 2004

This work has shown in the past that higher-order reasoning systems can solve problems of this kind automatically, but the complexity inherent in their calculi and their inefficiency in dealing with large numbers of clauses prevent these systems from solving a whole range of problems.

System Description: LEO -- A Resolution based Higher-Order Theorem Prover

- Mathematics, Computer Science
- 2005

The Leo system has recently been successfully coupled with a first-order resolution theorem prover (Bliksem) and is implemented as part of the Ωmega environment and has been integrated with theΩmega proof assistant.

Extensional Higher-Order Paramodulation and RUE-Resolution

- Computer ScienceCADE
- 1999

Two approaches to primitive equality treatment in higher-order (HO) automated theorem proving are presented: a calculus EP adapting traditional first-orders paramodulation, and a calculus ERUE adapting FO RUE-Resolution to classical type theory, i.e., HO logic based on Church's simply typed λ-calculus.

A Lost Proof

- Mathematics
- 2001

We re-investigate a proof example presented by George Boolos which perspicuously illustrates Gödel’s argument for the potentially drastic increase of proof-lengths in formal systems when carrying…

LEO-II - A Cooperative Automatic Theorem Prover for Classical Higher-Order Logic (System Description)

- Computer ScienceIJCAR
- 2008

The improved performance of LEO-II, especially in comparison to its predecessor LEO, is due to several novel features including the exploitation of term sharing and term indexing techniques, support for primitive equality reasoning, and improved heuristics at the calculus level.

Fast Clause Normalization for Higher-Order Automated Theorem Proving

- Computer Science
- 2009

The task is to develop a new and ideally improved OANTS architecture for the new LEO-II prover, which is currently using a primitive, sequential interaction model.

Functions-as-Constructors Higher-Order Unification

- Computer ScienceFSCD
- 2016

The main idea behind this extension is that the arguments to a higher-order, free variable can be more than just distinct bound variables: they can also be terms constructed from (sufficient numbers of) such variables using term constructors and where no argument is a subterm of any other argument.

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